Bibcode
Roger, Claude; Unterberger, Jeremie
Referencia bibliográfica
eprint arXiv:math-ph/0601050
Fecha de publicación:
1
2006
Número de citas
11
Número de citas referidas
7
Descripción
This article is concerned with an extensive study of an
infinite-dimensional Lie algebra $mathfrak{sv}$, introduced in the
context of non-equilibrium statistical physics, containing as
subalgebras both the Lie algebra of invariance of the free Schrodinger
equation and the central charge-free Virasoro algebra $Vect(S^1)$. We
call $mathfrak{sv}$ the Schrodinger-Virasoro algebra. We choose to
present $mathfrak{sv}$ from a Newtonian geometry point of view first,
and then in connection with conformal and Poisson geometry. We turn
afterwards to its representation theory: realizations as Lie symmetries
of field equations, coadjoint representation, coinduced representations
in connection with Cartan's prolongation method (yielding analogues of
the tensor density modules for $Vect(S^1)$), and finally Verma modules
with a Kac determinant formula. We also present a detailed cohomological
study, providing in particular a classification of deformations and
central extensions; there appears a non-local cocycle.